Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters

This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.

Fuzzy Adaptive Tracking Control of Uncertain Strict-Feedback Nonlinear Systems with Disturbances Based on Generalized Fuzzy Hyperbolic Model

In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.

EXISTENCE OF GENERALIZED SOLUTIONS TO A HYPERBOLIC MODEL OF COMBUSTION

In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.

Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect:Regular Waves

A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model＇ s performance on prediction of wave heights around breaking point for the wave motions in surf zone.

Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect:Random Waves

New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is gready saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.

Robust adaptive fuzzy control scheme for nonlinear system with uncertainty

In this paper, a robust adaptive fuzzy control scheme for a class of nonlinear system with uncertainty is proposed. First, using prior knowledge about the plant we obtain a fuzzy model, which is called the generalized fuzzy hyperbolic model （GFHM）. Secondly, for the case that the states of the system are not available an observer is designed and a robust adaptive fuzzy output feedback control scheme is developed. The overall control system guarantees that the tracking error converges to a small neighborhood of origin and that all signals involved are uniformly bounded. The main advantages of the proposed control scheme are that the human knowledge about the plant under control can be used to design the controller and only one parameter in the adaptive mechanism needs to be on-line adjusted.

Velocity profiles description and shape factors inclusion in a hyperbolic,one-dimensional,transient two-fluid model for stratified and slug flow simulations in pipes

In a previous work it has been shown that a one-dimensional,hyperbolic,transient five equations twofluid model is able to numerically describe stratified,wavy,and slug flow in horizontal and nearhorizontal pipes.Slug statistical characteristics can be numerically predicted with results in good agreement with experimental data and well-known empirical relations.In this model some approximated and simplified assumptions are adopted to describe shear stresses at wall and at phase interface.In this paper,we focus on the possibility to account for the cross sectional flow by inserting shape factors into the momentum balance equations of the aforementioned model.Velocity profiles are obtained by a pre-integrated model and they are computed at each time step and at each computational cell.Once that the velocity profiles are known,the obtained shape factors are inserted in the numerical resolution.In this way it is possible to recover part of the information lost due to the one-dimensional flow description.Velocity profiles computed in stratified conditions are compared against experimental profiles measured by PIV technique;a method to compute the velocity profile during slug initiation and growth has been developed and the computed velocity distribution in the liquid phase was compared against the one-seventh power law.

Effect of particle breakage on the behavior of simulated angular particle assemblies

Many attempts have been made to find various relationships for different parameters and some kinds of constitutive models for studying the behavior of particulate media. All these models are based on concepts of continuous media. Using a numerical method such as discrete element method, one can figure out what is happening through a discontinuous media where soil particles play the main role in introducing the shear strength and deformation characteristics. The behavior of the media with breakable particles is studied in this paper and compared with that of the assembly with non-breakable particles. In this paper, the hyperbolic elastic model is investigated for the assembly of polygon shaped particles in two different test series. In addition, evolution of different macro parameters of the assembly such as volume strain, angle of friction, angle of dilatancy and elastic modulus is studied during the simulation tests both for non-breakable and breakable soil particles. At the end, a parametric study is performed on the effect of strength of particle breakage on the assembly behavior.